Articles | Volume 8, issue 10
https://doi.org/10.5194/wes-8-1613-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-8-1613-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Extreme wind turbine response extrapolation with the Gaussian mixture model
Xiaodong Zhang
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Nikolay Dimitrov
CORRESPONDING AUTHOR
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
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Joint probability distribution of 10 min mean wind speed and the standard deviation is proposed using the Gaussian mixture model and has been shown to agree well with 15 years of measurements. The environmental contour with a 50-year return period (extreme turbulence) is estimated. The results from the model could be taken as inputs for structural reliability analysis and uncertainty quantification of wind turbine design loads.
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Cited articles
Akaike, H.: Information theory and an extension of the maximum likelihood principle, in: Selected papers of hirotugu akaike, Springer, New York, NY, 199–213, https://doi.org/10.1007/978-1-4612-1694-0_15, 1998. a
Arthur, D. and Vassilvitskii, S.: K-means++: The advantages of careful seeding, in: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics, 1027–1035, ISBN 978-0-89871-624-5, 2007. a
Barone, M. F., Paquette, J. A., Resor, B. R., and Manuel, L.: Decades of wind turbine load simulation, in: 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Aerospace Sciences Meetings, No. SAND2011-3780C, https://doi.org/10.2514/6.2012-1288, 2011. a, b, c
Cui, M., Feng, C., Wang, Z., and Zhang, J.: Statistical representation of wind power ramps using a generalized Gaussian mixture model, IEEE T. Sustain. Energ., 9, 261–272, https://doi.org/10.1109/TSTE.2017.2727321, 2018. a
Dai, B., Xia, Y., and Li, Q.: An extreme value prediction method based on clustering algorithm, Reliab. Eng. Syst. Safe, 222, 108442, https://doi.org/10.1016/j.ress.2022.108442, 2022. a
Dempster, A. P., Laird, N. M., and Rubin, D. B.: Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Stat. Soc. B Met., 39, 1–22, https://doi.org/10.1111/j.2517-6161.1977.tb01600.x, 1977. a
Dimitrov, N.: Comparative analysis of methods for modelling the short-term probability distribution of extreme wind turbine loads: Methods for modelling the probability distribution of extreme loads, Wind Energy, 19, 717–737, https://doi.org/10.1002/we.1861, 2016. a, b, c
Ding, J. and Chen, X.: Assessing small failure probability by importance splitting method and its application to wind turbine extreme response prediction, Eng. Struct., 54, 180–191, https://doi.org/10.1016/j.engstruct.2013.03.051, 2013. a
Ding, J., Gong, K., and Chen, X.: Comparison of statistical extrapolation methods for the evaluation of long-term extreme response of wind turbine, Eng. Struct., 57, 100–115, https://doi.org/10.1016/j.engstruct.2013.09.017, 2013. a
Ditlevsen, O. and Bjerager, P.: Methods of structural systems reliability, Struct. Saf., 3, 195–229, https://doi.org/10.1016/0167-4730(86)90004-4, 1986. a
Fogle, J., Agarwal, P., and Manuel, L.: Towards an improved understanding of statistical extrapolation for wind turbine extreme loads, Wind Energy, 11, 613–635, https://doi.org/10.1002/we.303, 2008. a
Freudenreich, K. and Argyriadis, K.: Wind turbine load level based on extrapolation and simplified methods, Wind Energy, 11, 589–600, https://doi.org/10.1002/we.279, 2008. a, b, c
Gupta, L. and Sortrakul, T.: A gaussian-mixture-based image segmentation algorithm, Pattern Recogn., 31, 315–325, https://doi.org/10.1016/S0031-3203(97)00045-9, 1998. a
He, X., Cai, D., Shao, Y., Bao, H., and Han, J.: Laplacian regularized Gaussian mixture model for data clustering, IEEE T. Knowl. Data En., 23, 1406–1418, https://doi.org/10.1109/TKDE.2010.259, 2011. a
Huang, Y., Englehart, K., Hudgins, B., and Chan, A.: A Gaussian mixture model based classification scheme for myoelectric control of powered upper limb prostheses, IEEE T. Bio.-Med. Eng., 52, 1801–1811, https://doi.org/10.1109/TBME.2005.856295, 2005. a
Jung, C. and Schindler, D.: Global comparison of the goodness-of-fit of wind speed distributions, Energ. Convers. Manage., 133, 216–234, https://doi.org/10.1016/j.enconman.2016.12.006, 2017. a
Kim, S. C. and Kang, T. J.: Texture classification and segmentation using wavelet packet frame and Gaussian mixture model, Pattern Recogn., 40, 1207–1221, https://doi.org/10.1016/j.patcog.2006.09.012, 2007. a
Moriarty, P. J., Holley, W. E., and Butterfield, S. P.: Extrapolation of extreme and fatigue loads using probabilistic methods, Technical Report, No. NREL/TP-500-34421, https://doi.org/10.2172/15011693, 2004. a
Naess, A., Gaidai, O., and Karpa, O.: Estimation of extreme values by the average conditional exceedance rate method, J. Prob. Stat., 2013, 797014, https://doi.org/10.1155/2013/797014, 2013. a
Natarajan, A. and Holley, W. E.: Statistical extreme load extrapolation with quadratic distortions for wind turbines, J. Sol. Energ.-T. ASME, 130, 0310171–0310177, https://doi.org/10.1115/1.2931513, 2008. a
Nguyen, T. M. and Wu, Q. M.: Fast and robust spatially constrained gaussian mixture model for image segmentation, IEEE T. Circ. Syst. Vid., 23, 621–635, https://doi.org/10.1109/TCSVT.2012.2211176, 2013. a
Permuter, H., Francos, J., and Jermyn, I.: A study of Gaussian mixture models of color and texture features for image classification and segmentation, Pattern Recogn., 39, 695–706, https://doi.org/10.1016/j.patcog.2005.10.028, 2006. a
Srbinovski, B., Temko, A., Leahy, P., Pakrashi, V., and Popovici, E.: Gaussian mixture models for site-specific wind turbine power curves, P. I. Mech. Eng. A-J. Pow., 235, 494–505, https://doi.org/10.1177/0957650920931729, 2021. a
Toft, H. S., Sørensen, J. D., and Veldkamp, D.: Assessment of load extrapolation methods for wind turbines, J. Sol. Energ.-T. ASME, 133, 021001, https://doi.org/10.1115/1.4003416, 2011. a
van Eijk, S. F., Bos, R., and Bierbooms, W. A. A. M.: The risks of extreme load extrapolation, Wind Energ. Sci., 2, 377–386, https://doi.org/10.5194/wes-2-377-2017, 2017. a
Wackerly, D., Mendenhall, W., and Scheaffer, R. L.: Mathematical Statistics with Applications, Thomson, 912 pp., ISBN 0-495-38508-5, 2008. a
Wahbah, M., Alhussein, O., El-Fouly, T. H., Zahawi, B., and Muhaidat, S.: Evaluation of parametric statistical models for wind speed probability density estimation, 2018 IEEE Electrical Power and Energy Conference, Toronto, ON, Canada, 1–6, https://doi.org/10.1109/EPEC.2018.8598283, 2018. a
Weber, C., Ray, D., Valverde, A., Clark, J., and Sharma, K.: Gaussian mixture model clustering algorithms for the analysis of high-precision mass measurements, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Nucl. Instrum. Methods, 1027, 166299, https://doi.org/10.1016/j.nima.2021.166299, 2022. a
Yang, Q., Li, Y., Li, T., Zhou, X., Huang, G., and Lian, J.: Statistical extrapolation methods and empirical formulae for estimating extreme loads on operating wind turbine towers, Eng. Struct., 267, 114667, https://doi.org/10.1016/j.engstruct.2022.114667, 2022. a, b
Yin, S., Zhang, Y., and Karim, S.: Large scale remote sensing image segmentation based on fuzzy region competition and gaussian mixture model, IEEE Access, 6, 26069–26080, https://doi.org/10.1109/ACCESS.2018.2834960, 2018. a
Zhang, J., Yan, J., Infield, D., Liu, Y., and Sang Lien, F.: Short-term forecasting and uncertainty analysis of wind turbine power based on long short-term memory network and Gaussian Mixture Model, Appl. Energ., 241, 229–244, https://doi.org/10.1016/j.apenergy.2019.03.044, 2019. a
Zhang, X. and Natarajan, A.: Gaussian mixture model for extreme wind turbulence estimation, Wind Energ. Sci., 7, 2135–2148, https://doi.org/10.5194/wes-7-2135-2022, 2022. a
Zhang, X., Low, Y. M., and Koh, C. G.: Maximum entropy distribution with fractional moments for reliability analysis, Struct. Saf., 83, 101904, https://doi.org/10.1016/j.strusafe.2019.101904, 2020. a, b
Zhang, Y., Li, M., Wang, S., Dai, S., Luo, L., Zhu, E., Xu, H., Zhu, X., Yao, C., and Zhou, H.: Gaussian mixture model clustering with incomplete data, ACM T. Multim. Comput., 17, 1–14, 2021. a
Short summary
Wind turbine extreme response estimation based on statistical extrapolation necessitates using a small number of simulations to calculate a low exceedance probability. This is a challenging task especially if we require small prediction error. We propose the use of a Gaussian mixture model as it is capable of estimating a low exceedance probability with minor bias error, even with limited simulation data, having flexibility in modeling the distributions of varying response variables.
Wind turbine extreme response estimation based on statistical extrapolation necessitates using a...
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